CN205192716U - Single degree of freedom vibrates experimental apparatus - Google Patents

Abstract

The utility model discloses a single degree of freedom vibrates experimental apparatus, it includes the attenuator, the balance, torsion spring, step motor, measure the light eye, instruct the pointer, the excitation pointer, the connecting rod, the ejection structure comprises an ejecting needle, the fixed bolster, the balance round has the even concave tooth of measurement that distributes, torsion spring's one end links to each other with the balance, the other end links to each other with the excitation pointer, the attenuator is U type structure, it includes flat part and the extensions that form from two terminal extensions of flat part, the flat part can the free rotation, two extend portion do not lie in the below of going up of balance, step motor links to each other with the excitation pointer, a pair of measurement light eye is located the balance both sides respectively, and measurement light eye is restrainted and to be detected the concave tooth on the balance, instruct the pointer to install on the balance, the balance, connecting rod and torsion spring fix at the axle of fixed bolster on one's eyes through upper and lower two thimbles as an organic whole, it has the magnet steel to paste on the attenuator, change area that the variable damping ware contains the balance in order to change the variable damping size through adjusting the attenuator position.

Description

Single-degree of freedom vibration experimental provision

Technical field:

The utility model relates to a kind of single-degree of freedom vibration experimental provision, and it belongs to theoretical mechanics, college physical experiment teaching field.

Background technology:

In " College Physics " with " theoretical mechanics " teaching material, all mention mass-spring system, a lot of vibration problem can be reduced to this mechanical model; This model can be divided into again free vibration, damped vibration and forced vibration three kinds of situations.And the experimental provision of existing close copy, because complex structure is huge, can not volume production, price also higher, lecture experiment can only be done, every bit manipulation person can not be allowed all to participate in.

Therefore, necessary the deficiency solving prior art is improved to prior art.

Utility model content:

The utility model provides a kind of single-degree of freedom vibration experimental provision, its objective is simplified structural modal, improve system architecture measuring accuracy and accuracy, and improve automaticity, automatically can measure the correlation parameter of system, thus promote operator to the perceptual knowledge of single-mode system forced vibration rule under harmonic excitation.

The utility model adopts following technical scheme: a kind of single-degree of freedom vibration experimental provision, it comprises damper, balance, torsionspring, stepper motor, measure light eye, instruction pointer, excitation pointer, connecting rod, thimble, fixed support, described balance one astragal has the recessed tooth of the measurement be evenly distributed, one end of described torsionspring is connected with balance, the other end is connected with excitation pointer, described damper is U-shaped structure, it extension comprising flat part and extend to form from flat part two end, flat part can rotate freely, two extensions lay respectively at the upper and lower of balance, described stepper motor is connected with excitation pointer, measure light eye a pair and lay respectively at balance both sides, and measurement light eye bundle can detect the recessed tooth on balance, described instruction pointer is arranged on balance, balance, connecting rod and torsionspring are fixed on support bracket fastened axle eye as one by upper and lower two thimbles, damper is pasted with magnet steel, change damper by damping adjusting device position and comprise the area of balance to change damping size.

Further, described recessed tooth is carved full on balance uniformly.

Further, described stepper motor produces positive negative angle, sinusoidal excitation that speed is adjustable.

Further, described damper is pasted with magnet steel, to provide linear damping.

Further, described light eye of measuring for a pair can measure current balance present position.

The utility model has following beneficial effect:

(1) the utility model adopts balance as quality, torsionspring is as spring, stepper motor is given driving and is done forced vibration, compact structure, take up room little, be easy to carry, operator operates by doing it yourself the perceptual knowledge can promoted single-mode system forced vibration rule under harmonic excitation, improves learning interest;

(2) the utility model adopts stepper motor as sinusoidal excitation, and improve excitation waveform fidelity, structure has carried out again optimizing, and reduces the friction force of rotating shaft, improves measuring accuracy; System carries measuring system can improve measuring speed and data precision, thus make sampled result and theoretical value closer to, operator can draw out phase-frequency characteristic figure and the amplitude versus frequency characte figure of Damped-Forced nth Order vibration by the data of record.

Accompanying drawing illustrates:

Fig. 1 is the physical construction schematic diagram of the utility model single-degree of freedom vibration experimental provision.

Fig. 2 is the circuit theory diagrams of the utility model single-degree of freedom vibration experimental provision.

Wherein:

1-damper; 2-balance; 3-torsionspring; 4-stepper motor; 5-measures light eye; 6-indicates pointer; 7-encourages pointer; 8-connecting rod; 9-thimble; 10-fixed support; 11-flat part; 12-extension.

Embodiment:

Please refer to shown in Fig. 1, the utility model single-degree of freedom vibration experimental provision comprises damper 1, balance 2, torsionspring 3, stepper motor 4, measure light eye 5, instruction pointer 6, excitation pointer 7, connecting rod 8, thimble 9, fixed support 10, balance 2 one astragal has the recessed tooth of the measurement be evenly distributed, one end of torsionspring 3 is connected with balance 2, the other end is connected with excitation pointer 7, damper 1 is U-shaped structure, it extension 12 comprising flat part 11 and extend to form from flat part 11 liang of ends, flat part 11 to be arranged on support panel and can to rotate freely, two extensions 12 lay respectively at the upper and lower of balance 2, stepper motor 4 is connected with excitation pointer 7, measure light eye 5 a pair and lay respectively at balance both sides, and light eye bundle can detect the recessed tooth on balance 2, instruction pointer 6 is arranged on balance 2, balance 2, connecting rod 8 is fixed on the axle eye of fixed support 10 on as one by upper and lower two thimbles 9 with torsionspring 3, damper 1 is pasted with magnet steel, change damper 1 by damping adjusting device 1 position and comprise the area of balance 2 to change damping size.The other end of torsionspring 3 is connected on excitation pointer 7.Measure the left and right sides that light eye 5 is placed on balance 2, the pulse produced when measuring the recessed tooth of balance need have certain phase differential.Control circuit inputs according to user, and can press setting regular movement by control step motor 4, excitation is added on balance 2 by excitation pointer 7 with connecting rod 8 by stepper motor 4, and excitation balance 2 rotates.

In the utility model, balance is equivalent to the quality in mass-spring system as research object, balance is carved a full circle recessed tooth of uniform size, so that measuring system can trace into the instantaneous position of balance, here escapement shaft configurations in similar mechanical watch is adopted, object is the friction force in order to reduce when balance rotates as far as possible, thus reduces system damping.Torsionspring is equivalent to the spring in mass-spring system.

Damper adopts magnet steel as viscous damping, can linear damping be provided, balance swing in magnetic field and cutting magnetic line time, produce current vortex in balance, thus generation damping, the magnetic flux area that rotary damper can change magnet and balance can change damping size.Exciting electric adopts stepper motor, is swung sinusoidally by stepper motor rotating rule, and swing (excitation) cycle and amplitude can arrange change according to user.Adopt two light eye of measuring to be conducive to metering circuit with the balance of the recessed tooth of band and to obtain current balance instantaneous position, thus the phase differential of vibration period of balance, response amplitude and response can be detected.When not adding damping with excitation, form undamped without forced vibration, metering circuit can measure the natural period of now balance; When there being damping to encourage with nothing, be configured with damping without forced vibration, metering circuit can measure ratio of damping; When having damping and have excitation, being configured with damping has forced vibration, and metering circuit can measure response amplitude and the phase differential of now balance; Amplitude-frequency response characteristic curve and the phase versus frequency response charac t curve of single free vibration can be gone out according to the Plotting data measured by above-mentioned data.

If accompanying drawing 2 is Measurement & Control circuit, mainly comprise high speed arm processor, key-press input and display module, motor driver and sensor input interface.Key-press input and display module provide human-computer interaction function, and key-press input can select mode of operation (undamped is without being forced to pattern, having damping without being forced to pattern and Damped-Forced nth Order pattern), and start and stop motor, starts the functions such as measurement; Display module by now mode of operation display balance instantaneous angular, maximum amplitude, cycle length, die-away time, Energizing cycle and measurement result, can comprise the natural period of shimmy system, ratio of damping, response phase difference etc.; Arm processor is by sensor input interface, collect two light eye signal, because the pulse of two light eye collection has certain phase differential, therefore measuring system can detect the current position of balance and swaying direction, for calculating the natural period of balance, the damping ratio of damper etc. provide important parameter; The all right direct-driving motor driver of arm processor, provides pulse signal, enable signal and direction signal, to input the rotational angle, rotation direction and the velocity of rotation that change stepper motor 4 according to user.

Please refer to shown in Fig. 1, suppose the motion vector of balance the moment of torsion M that torsionspring produces _k, the moment of torsion M that damper produces _c, the differential equation of motion setting up this apparatus system is as follows:

Wherein J ₀for moment of inertia, for the angle of balance, θ is the angle of excitation, and C is ratio of damping, and K is spring constant, and t is the time.

Order $\frac{c}{J_0}=2n,\frac{K\mathrm{\θ}}{J_0}=h\sin \mathrm{\ω}t,\frac{K}{J_0}={{\mathrm{\ω}}_n}^2,\mathrm{\θ}=\mathrm{\Θ}sin\mathrm{\ω}t$

Finally arrange:

Wherein n is ratio of damping, ω _nfor natural frequency, ω is excitation frequency, and Θ is excitation amplitude, h=ω _n ²Θ.

By above formula, we can show that this Equation of Motion meets Damped-Forced nth Order quality-spring system equation of motion completely, can show the Damped-Forced nth Order characteristics of motion very visually thus.

When motor is motionless, damper is the added-time (damper does not comprise) not, and now artificially give balance rotational angle, shimmy system is simple harmonic oscillation, and now system equation is:

This solution of equation is: in such a mode, press and start timing button, metering circuit will calculate balance automatically by time interval during zero point, can calculate natural period or the natural frequency of balance system.

When dynamic damping does not apply motor, now artificially give balance rotational angle, shimmy system is damped vibration, and now system equation is:

This solution of equation is: show that the vibration regularity of now system is the sine wave of decay thus, decaying amplitudes and ratio of damping have relation than n, and damping ratio has with ratio of damping c again relation.So just can obtain ratio of damping c according to decaying amplitudes.

If at a time t _k,, vibration maximum amplitude A _k, then:

$A_k={\mathrm{Ae}}^{-{\mathrm{nt}}_k}$

A is initial magnitude, through one-period T _dafter, system reaches another amplitude A _k+1,then:

$A_{k+1}={\mathrm{Ae}}^{-n(t_k+T_d)}$

The ratio of these two adjacent amplitudes is decrement:

$\frac{A_k}{A_{k+1}}=\frac{{\mathrm{Ae}}^{-{\mathrm{nt}}_k}}{{\mathrm{Ae}}^{-n(t_k+T_d)}}=e^{{\mathrm{nT}}_d}$

Taken the logarithm in above formula both sides:

$n=\frac{1}{t_k}ln\frac{A_K}{A_{K+1}}$

Namely ratio of damping n is calculated.

In such a mode, start timing button, measuring system will record the decaying amplitudes A of balance automatically _k+1with A _kwith time interval t _k, and calculate the damping ratio of damping system.

When there being excitation to have damping, now system equation is:

Non trivial solution is:

Wherein, one is damped vibration, is transient process; One next is steady-state process for forced vibration, by below one bring response amplitude and the phase differential that the differential equation can obtain system into.

Can Damped-Forced nth Order oscillating movement rule by the Energizing cycle of key change stepper motor thus under observing different Energizing cycle, now Energizing cycle is response cycle, and measuring system will automatically record and show response amplitude with the phasic difference of response (when namely encouraging by zero point, balance instantaneous angular now).Pass through following formula:

The phase differential ε of now system can be calculated.

The response amplitude of different Energizing cycle and the phasic difference of response under manual record, can draw amplitude-frequency response characteristic and the phase versus frequency response charac t curve of response frequency section.Namely single-mode system oscillating movement rule is can be observed by observing curve.

The utility model single-degree of freedom vibration experimental provision meets Damped-Forced nth Order oscillating movement model, can represent undamped without diriven motion rule, have damping without diriven motion rule and have damping to have forced vibration rule.Thus promote operator to the perceptual knowledge of single-mode system forced vibration rule under harmonic excitation, improve learning interest.

The above is only preferred implementation of the present utility model; should be understood that; for those skilled in the art, can also make some improvement under the prerequisite not departing from the utility model principle, these improvement also should be considered as protection domain of the present utility model.

Claims (5)

1. a single-degree of freedom vibration experimental provision, it is characterized in that: comprise damper (1), balance (2), torsionspring (3), stepper motor (4), measure light eye (5), instruction pointer (6), excitation pointer (7), connecting rod (8), thimble (9), fixed support (10), described balance (2) astragal has the recessed tooth of the measurement be evenly distributed, one end of described torsionspring (3) is connected with balance (2), the other end is connected with excitation pointer (7), described damper (1) is U-shaped structure, it extension (12) comprising flat part (11) and extend to form from flat part (11) two end, flat part (11) can rotate freely, two extensions (12) lay respectively at the upper and lower of balance (2), described stepper motor (4) is connected with excitation pointer (7), measure light eye (5) a pair and lay respectively at balance (2) both sides, and measurement light eye bundle can detect the recessed tooth on balance (2), described instruction pointer (6) is arranged on balance (2), balance (2), connecting rod (8) is fixed on the axle eye of fixed support (10) on as one by upper and lower two thimbles (9) with torsionspring (3), damper (1) is pasted with magnet steel, change damper (1) by damping adjusting device (1) position and comprise the area of balance (2) to change damping size.

2. single-degree of freedom vibration experimental provision as claimed in claim 1, is characterized in that: described recessed tooth is carved full on balance (2) uniformly.

3. single-degree of freedom vibration experimental provision as claimed in claim 1, is characterized in that: described stepper motor (4) produces positive negative angle, sinusoidal excitation that speed is adjustable.

4. single-degree of freedom vibration experimental provision as claimed in claim 1, is characterized in that: (1) is pasted with magnet steel with described damper, to provide linear damping.

5. single-degree of freedom vibration experimental provision as claimed in claim 1, is characterized in that: measure light eye (5) a pair and can measure current balance (2) present position.